Polymer Melt Rheology: A Guide for Industrial Practice

Polymer Melt Rheology A Guide for Industrial "'''''''1"'#.'''''''

Polymer Melt Rheology A Guide for Industrial Practice

F. N. Cogswell

Godwin Limited

ISBN 1 85573 198 3

2003FN British CaltaJc,gu:mg in Publication Data A ,-alACllVJ~Uv record for this book is available from the British All stored in a retrieval the Printed

PU[)Uc,atIcm may be reproduced, or transmitted in any form or any means~ Ath"""UftC"" without cQ[)vng:m owner.

ext.enem:e of of leI art of ~Y"£'C"'A;"_ pra,Ctlt:tODlers of that technology, and a o,eve:lot)eO academic contributors to this field. stimulation, this book is respe(~tttlllV lAn'!:l1"trnA."tCl

ba'~k:Q"rOlmd SCl~en(:e

PUBLISHER'S NOTE While the pnlrlCll)leS of careful sUl1tabtllty of caJI~uJ~itl(J.n not be form or contents person tnc;~re4::m.

in this book are the nr".l'tn.f'f' pulblis,heJrs cannot in the solutions to inl"llultill'!:lJ problems and any kind in of or out or any error reliance any

Contents

xi xiii

Notation Introduction

1

1 Fundamental concepts

5

1.1 2e('me~trv

of deformation rlleolof21cal response of materials

1.2 Thermal and tlle:rmtodymlmJic response

1.3

"'h\'lis,heci. from one OO.lvnler molecular of tenloeratlure which Because the of VIS'C05!ltv Table 3.1 compares that del:>endel!lce the different are cOlnmlonllv orocesse"l~::t1'~ and Evaluation of creep eXlpel"lm,ents under constant stress before

......

0.11'

l'

Time

3.6

Im~e-aepfmC.1ent

flow is

apparent Maxwell parameters

101'

Ph\J(,I,f'nl

Features

47

109 10· 107

/

/

106

/

/

105

G

/ 10·

/

/ 10- 2

Cvclic loading ~ (s/rad)

3.7 compan!mn of

established Maxwell pal~alTlet~~rs:

Creep loading (s)

and osc:lllaltOl:y shear flow:

at 20ne

allows the mtC:!fPret,ltlo,n of tllTle-cler)endelflt alDoBlrellt

otc.Ue:d as a function of time these cornmonlly have the form shown in

llelrWf~en

where stress and strain are n r.."nr\rt1nn!:l1 evaluation of as a first ani~UUU I1'eQUellCV and time texts, for eXclm1ple 1-

dies

(

1-0

formulae:

60 Swell ratio for Dies of zero

zero

."",.,,~ ..... ,

(vii)

( B.,Bb : (exponential

3.6..3 Converging Flows

In rnl'V""rOllno

of a an extensional flows are much more Jde~alJ:secl flows in the as to 1) that when two ","".ar'ln ... mtc~ra':tlOln and umloubtedlv ~hl'''~rllno and an extensional dallnting cornplex11tv if the full were made. a Quanltitaltive the strain rate histories shows that at the wall of the ,,""llnL"U"l1 is zero, the shear strain rate has its maximum and the extensional strain rate zero, while maximum strain rate occurs where the is at its maximum and the shear strain flow is sUJ)el1po~,ed

PfC12nlatic view thus aIJows us to COlDP'ute the flow as determined

One

the interaction between the flows addition of the shear and extensional

ilie

fur

cyfmdlrtcal flow: pressure where is the COfltrilt>utton due to to ex1:en:SlOlnal flow and

+ Sh€~arl!Dg

flow and

is the contribution due tan 8

where ro is rl is 8 is OSI is

n OBI

the the the the

die radius die exit radius half of convergence ,shear stress to the shear rate at die wall at the Yt = the volume flow is power in the relation:ship is the extensional stress average extensional tan strain rate, £1 =

1.1£.. , ..."",,1

Features and Flow

61

3.20 Extensional flow and sbearu12 flow in a .. "' ....""...,.1"1 die

shear is the dominant flow rel:atl()nSblp between flow rate COlnp()llelnt At about If

rate rupture, the At the becomes we

stn~tcl1liD1:t

mm

130 S-1

for streamline therefore whence

the half

tan (J = 2 x 7/130 = 0-1 of convergence 6 rI"' ....."',"'.,

62

Melt Rheology

were used to effect the whole of the reduction from 20 mm to the length of the would be such that 91L = tan 90 mm. For most purposes such a would be ex(;ee,om2lv long and would to Thus we a sut)SlCllaJ":V at what diameter is this "'ctor~"',..o.rlf·1 A taper would be 45° and so, since the 7 we have

i.e.

tan

r=

i.e.

7

we may dele1u(;e 14 = (4 x nr~,.tprrp,rI

m and ro=2·2mm die for this extrusion is one that reduces the overall Further optimisation may in be

by by

"'"..",""."' ... '1 ....... flow, swell ratio is taken as oOltential "'""..... ,...h........, ..." from """""'''1"''''''

and from extension; exp

ERI

COJrre:soCtndine to the stress at the die exit COlrre!mcfndine to the extensional stress at .... """,11""'''''

and dies with contraction from 0-01 to 1·57 for flow

U!:ll"'!t1'1i'"

value Pressure Swell ratio

deviation 16% taD.en:~C1

annular radial In any of I"'n1"''''''I" ...ii1'1O' flows it is necessary to bear in mind fact that the ex1:en:sioJnal vi!itl~os:jtv may be several orders of "'''''''!:li'.", .. than the shear thus, no matter how to the extensional should never be since it is which are likely to the stresses the material and so determine the quality

Phllr~' we of the structure. attribute the chain stiffness to the t1e'~ibilitv

ratio at 200°C above but variation so that the ratio From this we can deduce on the stiffness of the chain. the non-Newtonian of the as defined the shear the has decreased to one-half its low shear also varies with chain a correlation between non-Newtonian flow and orientation, is one The which seems least consistent with the H.lVUU.JlU.".

Polymer Melt Rheology Table 4.2

related to Molecular Weight: PoIy(metbyl methacrylate) at 210°C

Weigbt ... .,..,.n"...., molecular 34000 75000 160000 360000

2x1()4

600 16000 400000 8000000

30 x 1()4 8 x 1()4

3xl()4 2xl()4

tleJnlJlle comonomer in tenlJ)erature and so the ",,,,£,,,,,£,"tu and so is by flexibility of the lJac:klJ4one by the use of the comonomer, or by lDCre(llSllll.2 effective cross-sectional area of the molecule the of pla,stic:Js~'r the to an enhancement of nonNewtonian behaviour and so a further reduction in under any high shear condition. Thus, as a aplprc.xnnalt1011l, we can observe a common n~t't"U"n determined their cnt!ml[Cal ture. may in two ways: as a which to Drc~dic:t the of a melt from its chemical structure, and a of dependent on chemical and as a framework within more detailed to another. is not a rule consistent with an intuitive a01Pre:ci3ltloln eXlstelnce of such an empirlical to such a 'rule' and the~exc~pltlolns. and One such exception calculated that rodlike predlc1:lOn has

77

Xhleol

10 6

104

a

Stress (N/m2)

---'""1.""",---Stress concentration

/ b

~

Tension thinning

Tension stiffening

Necking

Uniform draw

strc;~tchin2 flow behaviour of linear (- - -) and branched MFI 0·3 at Istre b Effects of stress concentrations on flows

Thus similar in other tests may be a to stress extensional of to flows. The for the in increase with stress means that local stress concentrations are less

H.1l~eolof}.~v

and Structure

83

flow brears pr(,l)al)lv aSSOCJ,atc;~Cl with very CllSpeJ:SlOin at a 1 ~m level. The flow be deformed to an empS()lo. lDCre(]lStrl2 the surface area . That work to be but such work is recoverable on removal of the stress as the reverts to its it is desirable that the continuous so that work is more done to j:lrtuP"'p it is to construct a blend of a amount of 10vv~v]iscc)sl1:v with a small amount of this most

"'n ... "'t ...nrot ..... n vu.,uu,.:t.

u.", .....-u,d-"

86

.:...... .. ~

... "...~ ". ....

"

Shear stress (N/m2)

4.10 Blend of 66

InUJr_v1'i:t"n.~ihl

... "Irtn" ........

lOW'-Vl!,CO!mv

-

DOI,,,mers at 285°C

blend

cornp!Jnfmt. The

--

of blends is the concentration of the A review of the

-

,

"

\ \

10"

Shear stress (N/m2)

4.11 Effect of low Base 0·29 volume cone.

ratio filler MFI 20 at 130 C aspect ratio filler Q

f(hlf!OIC1.2'V

87

and Structure

mc)Ortlccltl()n, tend to increase the U1Co;,f"flC!ltU prc~po:seo to describe MalrOll·Ylerc:!e n~latl0nsllllf), that I have found eSP'ecI:aUv

"

",

---~-~ ...............

",

...

"

\ Stress

4.12 Effect of filler concentrations Base pol'ymc~r Low aspect ratio fiUer Agglome]ratc~d low aspect ratio filler aspect ratio fiUer

88 resistance to COIIIUloction with

Molecular

----~r;::;. lUb'ica1.1 Plasticiser Temperature

Log shear stress

4.13 SUlnmarv of factors afft:,ctiIlg the

Vl!i:(~ositv

of

pol~rmers

SpatC1l1lg out the molecules. Their most obvious effect is to tend to reduce the elastic modulus of the stress. The effectiveness of a platstitcisc~r cOIlcentI'ation, cOlnp:atit)ili1ty and "1C.(,l'\C~tf''I.1

or extenlau The effects of fillers the other factors mtluenC]lng

1'">-.,._.....,"', the mtJlueloce microstructure of the ......".£'1.. "'1factor, The pr(.ce~)sil1lg ht",t", ....,

gellerau~,eCl 'liQ,('ru~thl

with

89

structural is sometimes the shortest route to i"1~rit"l1tni(Y a situation. To this a simple measurement such as Melt Flow Index on base polymer and the end-product should be included in all studies.

REFERENCES

1. Courtauld Atomic

IYIUUta:s.

2. 3.

4. 5. 6. Morgan,

7..HU"I\.~U.

8. 9.

11,

10. Uraesslc!v

12.

14.

J

a\.uv li\..

15 .......... '.h'VU.

on the Structure

Journal

Pn/u.,...." ..

Science

90 19. C02:swell.

On the Formation oresented at the 1980.

Inrin"t,r'u

Molecule C:on:ferienc:e on

20.

22.

25. 26.

27. 28. 29.

30. sUS,peJIlSliOns from unimodal

31.

32. on fibre orientation in Journal Materials Science, 13,

"l(:f'n
95

Adventitious Flow Phenomena

Weld line

5.2

~el)afl:lttclD

and reVl1eldlin2 of flow past an obstacle

to millimjsiflg onenteo, but that OnC;!ntiCltlcm SllOSC~Quentlv Because the relaxation of order is a low the relaxation time of the materml--ttle A indication of the relative rel,aXattlofn to be of materials and under different conditions is to COlnp,are the characteristic time of the material with the time scale of the of Deborah Number low ratio indicative effective relaxation. 5.6 MELT MEMORY

The fact that melts possess a memory, rise to such effects as orientation and allows to remember non-uniform ctetects. of which and lumpy tre,QU(!ntJIV encountered. pa~;Slfllg an obstacle and rewelds downstream of that in the of the weld be

96 time for the relaxation of those local stresses. We may note that mcrealSll1Ul the of the reduces the rate of rel,aXfJltJO,n sec.anltIOfn occurs in the shear teJ111pt~ralturc~, nor pressure will ehInin.ate dlsltnbute weld such PflltlCl[)leS

i round ~ across

~ round

i across aU across

5.3 Weld distribution

means of a

mandrel

considerations The t>eJldlnf! of the streamlines under such if at die may cause the extrudate to bend or 'banana' an effect which may sometimes be nA ... " ...... "" the ...,&:•..." ....." of laminar flow fields. the case at the of oDmple:x and ""l"l1it'.1I'1'I;1

mtJrodluCltnf! a relax,ltio'n zone in the material's In all these cases the relmjrernell1t It matters not at all if that peJrturb,ttictn is small in to strain histories: some memory of it will as as the characteristic time of the material nPf'tnl't(! Features such as 'choke' ... o.,~."£""'''' and so in the process, and can IffiIOr()Ve wiJI do to relieve a heltero,g4em~OltS cannot be de!il,grled •...,.,,,....,. •.* 1, where a is coefficient of thermal dltfus;i0I1. x is the half or if it is fast envl~ ..... rto1rl'> surface from a loss to the texture of -"hal'''''''''',," be from a micro metre to several millimetres and of cmnp.araDle ampli1tude. The is if the able to ela.sti4:;allly so that skin can stretch and the stress SU[)SeICluc~ntJly relax wltholLit exlts may not, when corltarmnate the extrudate so pf()CeSSlm~,

Somewhat to this class of defect is an mstat)ll11ty front of an Here the front is Clllt'UPl"tp,t1 deformation 5.10) should the front rU[Jtture. tnrou:g:n. The burst is transmitted to the surface as a confer a decorative and the process of stress ......."'.I"A."'t1~ in a

5.12 COEXTRUSION INSTABILITIES

The search after desirable combinations of n ... np,rt" err"''''"11'n in coextrusion This tec:nnol(~2Y £ ...

have led to with it a new range

tenaeltlcy for a maltenal makes it erA ..' ...... ':1'II1.1

same

'l11,('>n,.i"u4L.

A

I

3

""

Shear rate

5.11 Inters,ecttnJ?;

vis,:ositv/~,he(u

rate curves of two oo)vmiers

Adventitious Flow

103

t'n4~nOtmt:~na

Shear rate profile

As combined

After extrusion (rod)

After extrusion (sheet)

5.12 Shear rate

may cause distorted interface

or lower than the main stream. If the two .....nl"I....,,"'".,." families such that their flow curves intersect difficult to obtain a SatlSnlct4Jry in a 'black box' and sut>sel(luc~ntlY StlblC~ctt:~(l driven flows nelcessal'UY A match elasticities interface may stress effects at the interface.

different

Secondary

Primary

5.13 """"JIJ""," formation where a

stream meets a 'weak' stream

104

Polymer Melt Rheology

'normal' stresses at the 'I1AI .....",,,h, dllSC()ntmullty for two streams of equal vi vf· .... ,-ilnSt and .rI""nt.lh"

1'h.,>",lr'..,."

of the

115

B

A---__'_, Shear stress Knieol~()~u~s

alPPJ'oprialte to different processes

ln1,pl'''u~n mCluHltn:l!:. while C is most aPI)ropn:ate to blow mClul(ltnll!:. "-'"......."....,.. 4 identified how these different may be attained. To out different are we may l"1Illu ideal to add fillers to the melt rather than to solid feeds.

120

Polymer Melt Rheology

dlsIPer:,e a small amount of low-viscosity material in a easy to thin down porridge by adding milk drc.ppine: lumps of into a bowl of milk and stirring n1"£'I,rhu''''' appetising result-the skills of are, indeed, c1e'.relc"lnf'~c1 in the kitchen. U1(!j"'n~:ihl__, t

6.3.2 Distributive Mixing Distributive mixing, aimed at is achieved by rows of the interruption of streamlines. on a screw or by the use of static flow. Distributive is of importance when the flow streams of different u.,,('One,.f'u and, more when those different viscosities are the result of 6.3.3 Homogeneity onllect:1Ve of all is homogeneity but nOlmogeIleI1:y is not mixing. A notable ex(;epltio1n lOtlrO(1uctlon of the which the solid separa'te from the melt the barrier flight, elements of the bed UlrlOUfl~n the extruder without melting. The barrier may break be nrt:~vent~ this and allows COJIS14deI'able increases in output rate to achieved. In the flow of ma'tenals, hOInO~tenc~ltv det,emls also on f'",,",n"'1"af'II11"'" the final flow to tp",np1"tltII1I'P to increase in the same way. the die This nalrf'f~.lhl tenlPeratlure build-up due to heat n ... r''''1''~:lht'.n and prOlmOttes which is more stable. n1"{"t1n,('f'

6.3.4 Work Input work input. Excessive work input is it All kinds of If the work input may also lead to heat generation and to is uneven it may indeed be a source of in the wrong it may defeat the of the or unwanted attrition. There are many the work input during UUJ'nUI"', but the in the final analysis, on the lOQ~re'llents to be mixed.

121 6.4 CONSTRAINED FLOWS

ConstlralIleCl flows are of two mOIV1Jlli! surfaces and pressure of r.Ollvp:vn1UJ 6.4.1 Screw Extruders

In the barrel of a screw extruder the flow is a COlnplex In the power reomr,em,ent ovi'..... , ...,.,.. the flow between the reilltiv'eiv t'n('1,Vll1,O' where shear rate = where D is the screw diameter H is between screw root and barrel wall N is the screw in revolutions per minute. The shear rate extruders is of the order 10-100 elements of the those which pass between the screw flight and at very rates. The resJICleJIlCe time of melts in the a screw extruder is of the order of 100 a total average of the order of 3000 units of very considerable flow purposes.

6.9 One unit of shear

In

dies and the nozzles of 10 I,ectlon moulCl1Oe; machines the flow is rates at much The shear rates in such flows have described in an kn'i1(! one in ISOllatlon. is where P is the pressure a bubble of radius r and wall thickness h. The volume of to the volume of the remains constant:

where 2R is the distance between the c\1"lcnn~1 nucleation sites. And so we as an aplpr<J,xnna1tlolll, stress

"23

n""'CCII ..':> remains constant, the stress bubble size increases. characteristic allows which is eSt)eClaJJIV e:"ag;gel'ate~d than smaller ones-a deformation decreases with stress. In we observed that branched materials have a resistance to deformation which increases with stress a more uniform cell that such materials should resistance to also tends to increase with stress if carried out more when the material response is more

6.5.2 Film Blowing and Casting, and Blow Moulding

more terlslcm-stlJttell1lnig the more elastic is In the extrusion Co(ltnlig nrnl"':>cc sus;celDtlltJle to 'neck-in'. In blow mouldme

process deformation is dOlmUlaI1ltly elastic. Both these courses lead inevitstress and so to the of balance to are a delicate one. The ODltlOllS !t111!tIII!thilp to stabilise a of may not available. in the defer to the advice of the However the context, we must Bard: .. , 'twere well it were done '1'" 1'1 ...........

6.5.3 Vacuum Forming

One process which is almost ",nt', .. where a sheet is sucked into a the most extreme tlnlwllnf! are at their minimum thickness and strain

process, of the

",hl

6.16 Vacuum

IOflrnl11lg

Polymer Melt Rheology

the sheet. In this process the stress is limited to about one atrnO!)pJ1lerc~, (rlh) x for processes, rlh::::::: stress for the nl"r\l"p,~" level of 1()6 The ideal response for a material in such a process would allow extension to strain and rapid after that. The aVf~ra~fe in the much less than the maximum strain reached in the average draw in a vacuum maximum draw in the corners material would tend to m(mJlriUJIl! into the corners, leading to more even

I

6.17 Deformation response in vacuum

toflmlllig

Ideal Conclusion Free surface strletcDJI1l2 to achieve thin sections: an to achieve enhancement important sec:onoalry oblf~ctllve may orientation, on the response of the melt. 6.6 BULK DEFORMATIONS

but cnCllngC;!S of COInOlres~)ed per

is al"~111111~1_ such an optias PY{"P"':IVP the quality usually better than that of nl"l"""11rp

in building up or relteasin2 dlsplacernellt from an accumulator

in

6.18 Observed

nmlla-tln

to

predeternlJnc~d

flow rate

aettencls on the volume of the acc;unlul,atofr--a the accumulator will ..",... relaxation will be more prc:deterllDiIled flow rate. Bulk cornPl'ess,ibillity :>Ilt",

Heat from the surface a moulded or so first. As the molten interior shrinks it exerts a force that an outer shell onto the solid skin, That force may the surface to buckle or or, if a be the the skin is melt. If that tension the melt may cavitate.

, ..7 SELECT BIBLIOGRAPHY In this Ch,lptc~r between and pr()CeSSJ10e:, nre:seIlt across a wide

t'rul1cIJ)les of roti:ttl(J'nal mOuIOIne: 1972.

Extrusion ~xt'·UJll,(Jn.

Van

H.F. Fiber and Yam

Polymer Melt Rheology

130

Film Blowing P. L. and Huck, N. D., Effect of .,.n...1"....l1c1nn variables on the IUDiOalnel'ltaJ orooerties of tubular 26 114-120 and 26 1961.

moulctme: SYll!1p()S1l1m,

Transactions

the ." .....

1975. C;alen(JrraR.~e,

. . . '.. "' ........"" Francais . .

PL....... ,,.,"',,

et

1 '• •;

131 REFERENCES

lDl lect:lon

1.

2.

m()tul(llDJ~.

Plastics and Rubber

Effect of extrusion variables on the fundamental Dollve'thv'lel1le film, 26,

3.

4. 5. 6. 7.

in Journee Apph1,.,,.., of extrudate rnC~Ol~()JUCal information. apl:Jropnate for studies. made under non-laminar flow c.11sUnJ~Ul:sne:c.1

as

REFERENCES

of molten

3. 4. 5. 6.

Ch~lUtf!ourleaux.

Aottend.ix 2

Interpretation of Extensional Viscosity from Flow through an Orifice Die

A2 Extensional flow

thrlom~h

an orifice die

def:orrnation is 1'3"."""__ ~'" flow received most use and " ' ......... L_

so

a

...... 4

eIoln2~iti(J'n

value has been

rate, i = at a flow rate of = '1 is the n is the power law

r

Polymer Melt If this

is to the orifice .... r"."" •• rt3 above the U!:Ilirtii'u of the intC:!fPret:ati<m flow measurements is be treated with caution. more tUflC1alm(mtaJ C1Dniunlatlon

l(n~f!Ol(1JlV

must be taken over the method is a transducer

.... r." .."'rr""rI

elcmg;atlonal response from i"i"I1!1Vl"rcrllncr results so obtained must or

REFERENCES

1.

COl1l1ptlabon, Journal

A01penlClIx 3

The Inference of Elastic Modulus from Post-extrusion Swelling

Several authors have sU2,ges:teCl intleroretinJ! DOI~t-c:~xt]rusllon able deformation. If extensional flow is then it is apl)rOpnate orifice flow as recoverable ex1:enlSlOltl, is the ratio of extrudate/die Olame:ter

SWf~lllIU!

+ leadmlJ! to extensional mo,duJlus.

E

+ swc:mUUl ratio from a

] die and

rR is the recoverable shear at

144

Polymer Melt Rheology

1/

6. 0

5. 0

.0

.0

L ./

.0

/

/

V

/

/ V

V

,/

.0

/ ~

/

1.0

1.2

1.4

1.6

1.8

2.0

Ratio of solidified extrudate to die diameter, BL

A3 Plot of recoverable shear

swelling ratio

There are several possible ways of making a measurement of sweHllnil ratio. One method is as follows:

L The extrudate is cut flush with the die. is obtained which may be transferred to a water bath to facilitate cooling. 3. The diameter is measurea with a mlC~rometer in two dtrc~cUons at right angles end. within 1 cm of the 4. The readings are and the result is taken as the extrudate diameter.

2. A new

Swell ratio is the ratio of extrudate to die diameter. Certain corrections would be necessary to obtain a true sweUllnil ratio. These arise from: on CO()11I112 under

ShJrinJka~~e

Sa~~2lfI2

to h'~'~7'lnn Diametral increase to surface tension flow conditions not established mutually carlcelUIll2 is that a These errors are, to some meaningful measurement can be obtained if the folJm'JlinlD CC)nClltlC)DS are met:

AD.Del1tarx

4

dI8.me:ter to die diameter >5: 1. when

REFERENCES

elastic deformations in polymier melts. Plastics and

.R.ppel1lOlX 4

Rupture Behaviour

Most observers now at the stress COlllcc:~ntlratJlon of flow into an orifice as a str()n21v e:x:tension:al of 'melt through stress at which the melt rUt)tUlres.

Yolvm~ers •

AP1penl(llX

5

Data Sheet for Capillary Flow

Extruder

Die diam. 2R

N/m 2

y=

0so =

By courtesy of lei Limited (Plastics """1"1;:>''''''"1

Ns/m 2

1/=

147

AD.oen:au 5

Extrudate N/m2

G

+

L

E=

Extrudate

o

APiDel11(11X

6

Comparison of the Rheological Properties of Two Samples of Low-density Polyethylene

Fl(ltlres A6.1-6 COD1D3Jre

same as

Cone and plate rheometry 103

10·

Shear stress (N/m2)

shear at 170°C

10- 1

Angular velocity (rad/s)

A6.2 nvnalnlC viscoelastic

nrClnp'rti,"'''

at 170°C

The elastic modulus results recovery on a cone and inference of elastic response from Dost-«~xtJruslon swell:mS! cone and plate measurements at low stress are agreement with dynamic measurements and with the normal stress measurements in flow A6.4), on the assumption l that re.~o"erahle

shear

N

E

"-

Cone and plate recovery measurements·

~

(!)

0' :::J

"5

10'-

"0 0

E "CIS Q)

.t::.

en

--10 3

10 4

Shear stress (N/m2)

reSl)On:se at 1700C on work of S. Citroen at UCW 1979 Orifice die G == E/3 where E is the elong,ltional modulus

150 Table A6 Data for Post-extrusion Swelling

10 30

2-0

1·5

2·4

100

2·7

1·7 2·7 distorted

~

/

2·6

).;'

If V

'/

I

"

10'

Stress (N/m2)

A6.4 First normal stress difference at 17WC: results of P. J. Daniells2

Non~laminar

flow

104Stress (N/m2)

A6.5 Orifice pressure

from

",a ...iU",r'l1

flow at 1700C

AO,oen:dLX

6

151

CD Ii..

:s ....Q.

3 x zero shear viscosity

.......

-

:s

-1-- __

----!---- -'"- ~~ I 10- .......

a: •

1 .....

.....

I "',

Based on orifice flow

103

104

105

Elo'ng4!1tiCtnal stress (N/m2)

A6.6 Elcm2;lltiornal flow at 170°C

REFERENCES

Elastic MSc

L.tUIUI"u,J,

1964.

Rubber Te(;hmcJlotzv 1977.

Appendix 7

Typical Processing Property Data for a General-purpose Low-density Polyethylene Polymer with Moderate Branching

Melt Flow at

2-0

5·3 x Table A7 Temperature

Density

Bulk modulus

Heat content relative to lCrC

3·1 130 170 210

Table A 7 lists diffusivity data

Heat in adequately per

762 746

1·10 1()9 0·96 x 1()9 0·83 x 109

±10

±0·03 x 1()9

Coefficient of tbermal dilTusion

x lOS

3·8 x lOS 4·8 x 105 5·8 X 105

1·1 x 1·1 10- 7 1·1 x

lOS

±0·1 x 10- 7

±0·1

bulk modulus and also beat content and tbis polymer. otber tbermodynamic data we bave

is cOl1l1plc~x near tbe but witbin tbe melt from above to below 70°C tbe beat eX(:hall1~e a of tbermal diffusivity of 1·1 x 10-7 m2/s

AO,rJen:atx 7 tel1[lpe:rat:un~s

above the while may tend to SClliSlc'n may dominate. These are minimised by the exclusion

coc~ftjlcleJr1t

of friction rises from a value of 0-4 at 20°C to a and then faUs to a minimum of at of about 0-45 as the polymer melts.

N

E -,

~

Q.

...0 "a ...:::J

10"

II)

fII

:...

Q.

II) (,)

!E ...

}I~ -1-_--

0

10&

104

Stress

of a oprlpr~ll_nnrT'ln~p Dol.vethvllene with moderate oranctlung

A7

Swell ratio at 15(f'C

10

100

(N/m2)

1·4 1·6

2·1 2·5

of

Appendix S

Typical Processing Property Data for General-purpose Grade Polypropylene Homopolymer

Melt Flow Rate neD'atj"e

3-0

mcrealses the and its effect may be corlsJdlen:~d as a such that

t"~'n1",\~"":lt"'''A

=S·6x on

uuu'nc't'tu

as reclucJing tenlperat1ure

Table AS Temperature

Density

Bulk modulus

Heat content relative to 20°C

Coefftcient of thermal diffusion

0·76 x 109 0·70 X 109 0·67 109 0·61 x 109

0 4·5 X 105 5-0 X 105 5·6 x 105 6·3 x 105

1·4x 0·9 X 10- 7 0-9 X 10- 7 1-0 x 1-0 10- 7 1-0 x

±0·03 x 109

±0·1 x 105

20 180

200 220 240 260

±1O

Table AS lists nAnC!li'u bulk modulus and also heat content and thermal diffusivity data for this nolvmler cornOl'esSlon or de(;Orrlprc~ssion: = 2·2 x 10-7C>ClNm-2

Pressure bmld-l1n/lrele:ase

ne~lttnlg

or

CO(U1n:2

at constant volume:

Polypropylene which melts at 165°C as a melt. presence of intense stress may the of sut)erc::oollin,g. most purposes it may assumed that polypropylene will

at

Aooelltau 8

155

water. The coettlcllent of of ooJvoJ'no'vlerle other this value can be very

Q,

...

0 "0

106

...::::J

Q)

fI) fI)

...

Q)

Q, II) (J

!E

105

0

.-
.,..c... t'(1

atnl0sphc~nc

AIO. bulk cornPI'eSS,lOn 1·2 x 10- 7 °C/Nm- 2

±0·1 x 10-7

at 20°C. The melt heat content

Quc~nCJllea

159

10

AO.oen:QlX

melts at about may SUI)er·cO(). of orientation 1"&:!>t'ilnt",:o", by a reversible cOlule:nScltlcm so that eClllilibri1Llm water content are reflected chja.n~~es in molecular nylon 6·6 may to thermal Above Drc;~sellce

The coefficient of kinetic friction at 20°C is about but falls l"'.U"urlll" to 0·1 in the Above 200°C friction to a maximum to a value of O· 25 at 250°C.

N

E

~

e.

0 I"0

106

I»

:; rn rn l-

e. I» (,)

-.: 'C

105

0

.< C 0 '0 c:::

W 104

C

V

/ /

I»

/ /' ",

",

"...

.....

,/

1; and Ell

/'

-

:

0

... '0...c::: I» )(

)(

I»

I

c: ea

"0

s;::-

ea 103

t.:

ea

I»

.c: rn

.S N

c:::

A

ci

.: ea

I»

.c: rn

-----

.S N 102

-E

rn ~

I

I»

I»

"0

E

~ rn :s

~

:;

"0 0

:e

it

~

10 5

106

Stress (N/m2)

AIO

KDleOI4Jgy

of an

lnl,F>l'i'1Inn

mouldinJZ

of 6·6 nylon

APtJen(lllX 11

Typical Processing Property Data for an Injection Moulding Grade of Polyethersulphone

VIS(;OSltv on pressure is such has the same effect on v ......,.tu 'l1 • •

6·7 x Table All Temperature

Density

Bulk modulus

Heat content relative to

20°C

+10

1·4

1()9

4·7 x lOS

±0·1

9

±0·3 x lOS

10

Coefficient oftberma. dltTuslon

±0·1 x 10-7

heat content and thermal crO~):SllrIK

after orolon2ec:l exposure to telTlpelratllLres

11

161

-

N

E

~

Q.

0

"-

"0

106

f

:::s en en f.)

"-

Q.

E/3

f.)

"

Ot: 't:

--

106

0

t
15mm

2·7mm

n=O·3 To

equation

(247)O'31~"""""0·82 whence

12·3 mm.

Author Index the

Ballman, R. L. Barrie, L T. 1 130 Bartos, O. 98 Benbow, J. J. 18,19 101,102 Berens, A. R. 10 (13) Berl~ol12:oni.

A.

32

tOllc')wuzg in Darlenth'l!St!3

56 (38)

104 (110)

Bird, R. B. 1 (4), 52 BloodeD, D. J. 97 L. L. 104 D. C. 52 Bol1ltinck. W. J. 32, 33

Daniells, P. l.

35

H.C. 47 93

Borocz, L.

Edwards, S.

73

E. 91 Busse, W.F.

~lI":Ui:lu.R.

Caron. I. M.

,cVC;;li:ljl!,C;;,

A. E.

102

H.

Cancio. L. V. Casson,N.

R.V. Chauffoureaux, J. C. 136 Chen,S.l. 120(131) Chen, Y. 87 (90)

Choi, S. Y. 44(68) Christiansen, R. L. 52 Oark, H. O. 58 P. L. 33 105

40

113

130 Oallo, R. l.

64

47 (68)

174 Kratz, R. F. 52 Kraus,G. 84 Krul, N. 32,33 Kubat, J. 93 Kuhfuss, H. F. 11

Galvin, P. 21 Gieniewski, C. 104 VU111:>1:'1::>. A. 84 Gottfert Feinwerke-Buchen 32 Gould, R. W. 10 50 Ura,essliey W. W.

34 58 102,103 (109),

84

Hessenbruch, H. Hirai, N. Holdsworth, P. J. 97 Holmes-Walker, W. A. Hoiomek, J. 136 Hori, Y. Howells, E. R. 102 Hubbard, D. 49 Huck,N. D. 113 Hudson, N. E. 32 Hulimann, H. P. 101 T.W. 98 Hutton, J. F. 20 Huxtable. J. 87.88 (90) Ide, Y. 23 ..... ,"""u... Chemical In(j!ustrie:r-Welw~rn Garden 54 91 Ito, K. 44 Ito, Y. 52 Jackson, W. J. 11 Jacovic, M. S. 83 J. C. 64 (70) Janieschitz-)'rie:gl, H. Johnson, J. F. Jones, T. E. R. 18 Jung,A. 44 Kamal, M. R. 138 Karl, U. H. 44 Kase, S. 32 Khan, A. A. 103 Klein, I. 129 W. 101

76,84

130

104 (110)

49,

Lamb,P. 32 97,98,99 Lamonte, R. R. Landel, R. F. Laun, H. M. 23 Leblanc, J. L. 34 Lee,B. L. 93 Lenk, R. S. 1 A.S. 7 Lord, H. A. 130 Lund, J. K. 32 Maack, H. 104 Macdonald, I. F. 47 McGowan, J. C. 44 McFarlane, F. E. 76,84 McJ!Celvlev J. M. 1 Mackie, P. 32 Mackley, M. R. Maerker,J. M. MaiUeffer. C. Markovitz, H. Masken, S. G. Matovich, M. A. 104 Matsuo, T. 32 Maxwell, B. 21,24 Meier,D. J. 84 Meissner. J. 20 23, 32 Mendelson, R. A. 40 (67) Menges, G. 94 Men, E. H. 98 A.P. 98 Metzner, A. B. 32 Mewis,J. 87 Middleman, S. MilIer,J. C. 104 Miller, W. R. Minnick, L. A. 18 Moore, D. R. 47,52 "UV'I.!f,GU, P. W. 76 M.E. 98 Nakajima, N. 130 Nazem, F. 20 (36) Newman, S. 86, 87 (90) Nicely, V. A. 76,84 Nielssen, L. E. 1

84

130

47

83

52

97

175 Schulken, R. M. 18 Scott Blair, G. W. 5 W.E. Semljonl[)V V. 44 Shah, Y. T. 99 Sbc:t>bc::rd. G. W. Shida, M. 141 Shishido, S. 52 Shroff, R. N. 141 Smit, P. P. A. 84 Southern, J. H. 97 A.J.B. 87 J.A. 32 J.E. 97 Swerdlow, M. S. 32,33

86,87

136

den Otter, J. L. 34 D.F. 67 Y. 87 " V i t l • .,..,,,, . .

J. 62 Paul, D. R. 86,87 Pearsall, G. W. 58 Pearson, J. R. A. 1 129 C. 44 Petrie, C. J. S. 23

55

J. M. 10 50 Plazek, D. J. 52 Plochocki, A. P. 86, 87 Pollock, D. 83 Poolak, T. 83 Porter, R. S. 44 Prest, W. N. 85 Pritchett, R. J. 62 Proctor, B. 96

130

104

104

Tadmor, Z. 94 Throne, J. L. 129 Tordella. J. P. 98,100,101 Trevena, D. H. 49 Truesdell, C. 5 Turner, S. 87,88 Tyabin, N. V. 57 Uhland, E.

85

98

97 98

H.

Raadsen, J. 84 Rabinowitsch, B. 135 Ra~:upa,tbi. N. 52 Rao, A. 129 Reid, G. C. 18 Reiner,M. 5,8 Reinhard, R. H. Rheometrics--Frankfurt 18,23 Rice, P. D. R. 62 130 van J. 136 Rokudai, M. 53 Rubin,1. 130

L.S. 136 Walters, K. 15, 18, 19 Warner, H. R. 52 Wasiak, A. 97 van Wazer,J. R. 15,19 Webb, P. C. 130 Weeks, J. C. 18 WeilsSellbeJ]t, K. West,D. 98 Westover, R. F. 33 White, J. L. 23 87 93,97 18

Schmidt, L. Schowalter. W. R. 64 Schrenk, W. J. 104 Schroeder, E. 83

49,50

104

Whorlow. R. W. 15,19,21 Williams, G. 130 Williams, M. L. 40 Willmouth, F. M. 97 Winter, H. H. 57 Wissbrun, K. F. 105 Worth, R. A. 58 Yearsley, F. 72 Ziabicki, A.

97

50

26

25

58

Subject Index

Adhesion 21,56,101,118 Weld lines

26 63,95,96 screw 120 10,78,84,93 11,12,54,63,65,79,104,105, 112,115, detailed studies 130 52,81,84 Bulk coolpre:ssi(JD

55,100,124 detailed studies 130 E '"".... 11 ..... ," H ....,_, rheometers 24, 146 amranlta2ces and limitations 34 errors and corrections 56 Cavitation 54, 107. 129 Chemical 11,41,92 Chemical structure 2, 71 Choke sections 96 Cluster flow 83 Coextrusion 102 Compression moulding 112 Cone rheometer 19 advantages and limitations 22 Contamination 50, 67, 104, 107 2 100

1,111 106,114,119.123 Data representation of 18,28, 146

152-163 spaces 11,61,92,101,114 Deborah number 48,95. 127 11,35,92,102,120 Density 9, 10,54, 106

2

'Draw resonance'

104 Shear, oscillal:ory

adventitious effects of 94 de)>endelrlce on stress 51 enhancement 97 inferred 30 in filled systems limited 52 measurement of 22,28, 143 of 104,127 see also M(J.duJlus; Orientation; Strain recovery Elc,ngliltioinal flow, see flows 11,150 Entropy 44 5 Strt~tcl:ling flows Extrusion 12, 56, 100, 121 detailed studies 129 of monofilament 61 58,63,167,170 105

11,51,54,91,93,97,104,126, Fibre 127 detailed studies 129 Fillers 10, 87. 102, 119 Film 11,12,34,51,53,54,65,93,104. 113, 127

177 Normalstress 7.19,20,103

detailed studies 130 rupture in 15 Film casting 11,104,127 Flow 32 9, 54,126 Fourier number 9 Friction 113 Gelation 35 Gell)m4~trv of deformation 54 Heat transfer 9. 34 at surface 10 34,50,53.81,93,120 114

10,11,34,52,53,54,55, 56,67,100, 107,112,115,121,123,128 detailed studies 130 orientation in 46,54,81,94,118 Instrumentation 2,34,39,133 94 crystal 10, 76, 83 Lubricallts 88 Maron~Pierce

87

Maxwell model 8, 18, Mechanical 32,53,83,84,88,97,105, 133,139 Melt Flow Indexer 33 'Melt fracture' 100 see also Non-laminar flow 92,113 52,75 definition 8 Molecular dimensions 73 Molecular models 71 Molecularstructure 2,71 Molecular theories 11 73, 77 distribution 52, 73, 78. 102 11, 71, 83, 91,133 'Neck-in' 106 Newtonian behaviour 8 Non-laminar flow 31,50,56,97,99,100,114, 139,145 Non-Newtonian flow 2,22,40,47, 75, 76 de~~n(lenc~onmo'leculajr~ej21~t

79

Orientation 3,21,46,52,54,58, 118 Orifice flow 30, 141 U~ciHlrdOlry flow and short time-scales 47 superposit:i.on on steady flow 47 Shear, oSCliJlatory

75,91,94,

111 Ph~ ~para1tion

93 88 Poisson'STatio 52 42,45 42,45,76,86 data 158 98 42,45,85 Pol,ydime1thyl siloxane 45,76 42,45,16 data 160 Polyetl~ylc;~ne, branched 3,29,42,44,45,48, 50,55,61,81,83,86,106,113,111.148, 167 Plastici~rs

42,45,71,74,80,81,98 42,45,16,83 74,78,85 Pol;v(meth:yl mlethacr:vlatle) 40,41,42.45,58, 83, 167 11,76 Polyptlen:ylelle oxide 45, 85 30,42,45.74,83,86,97,98,

74,83 10,42,45,50,53,74,83,91 Droces!~in2 aids for 10, 50 typical data 162 Post~extrusion 21,30,93,94,91,105, 143 32 see also Mechanical Pressure 44,96,97,137 43

178 Rabinowitsch correction Reclaim 11 Rheometers classes of 16

135

concentration 82, 107 overshoot 20 Stretch rate

125

123

35 in fibre and film coDilparisc1n of data from different 148 purposes of 15

112,113 detailed studies 129 8,15,49,93, 127,145 67

Sandwich

11,34 Screw extruder 56,57,113,121 as rheometer 34 effects of scale 11 twin 125

instabilities in 24, 52, 104, 127 rheometers for 23,32, 141 Structural foam 91 Structure, see Chemical structure; Molecular structure; MClrpll0l«lgy 91, Surface Surface 31,99,101,104,105,106,114 Surface 133 Surface tension 51 Swell ratio, see Post-extrusion

and 20 3, 11, 71, 79, 88, 91, 97, 134 97,101 Shear 6,56

see Viscous diSlsiplilticln 17, 18, 19 57 52, see also Non-Newtonian flow

oSClillatory

Shear rate forbidden 98 in 125 in extrusion 121 in 121 in screw extruder 121 Shrink 3 Sink marks 91

115 Slip 23,98,129,136 see also Adhesion Spaghetti model 52, 73 heat 9 mandrel 96

93 Strain 6 rateof 6 recovery 8,19,21,75,79,143 Streamlines 32, 100, 101, 114 Stress 6,49

126 52,81,125

39,41 75

transition

99 TeDSCIr notation 7 Thermal diffusion 9 Time 46 of 95 natural or characteristic of material

48,75,

95 natural rbeometers 35 Transients of stress and strain

11,34,48 19

54,65,104,127 32 oatcn-i[O-[)aI(:n variation 93 dellendellce on stress 52 common materials 7 Viscous dissipation 9, 10,23,41,56, 120, 137 Voiding, see Cavitation Voigt model 17

3,52,81,107,124 3,11,93,95,96,114,118,133 116,123

11111111111111111111111111 9 781855 731981